The UCSB Directed Reading Program (DRP) is a selective mathematics mentoring program in which graduate students or junior faculty members mentor undergraduate students in reading and research projects.
Paired based on mutual interests, groups will then work together during the Winter and Spring quarters (16 weeks) to produce a poster to be presented to colleagues and those residing in the College of Letters and Sciences.
Please note that due to the pandemic, this experience was fully virtual.
More information can be found at the following link.
This project explores the relationship between the Mobius Function, Mertens Function and their connections to the Riemann Hypothesis and Prime Number Theory in a 2-person team over 16 weeks.
After accepting our invitations to program, students of similar interests (ours being Analytic Number Theory) are grouped together.
This was our first time meeting our mentor - David Nguyen, a 6th year PhD student and the head organizer of UCSB’s DRP and each other. Though we look super serious in the photo, the group meshed well! \[ \]\[ \] We then decided to split into two groups so we could explore more topics - Tien and I (pictured on the right) became research partners and later good friends!
After first exploring on our own, then as a group of two, finally Tien, David and I decided to narrow our focus to the following topics: Riemann Sums and the Mobius Function.
We also choose our book, Graduate Texts in Mathematics: Problems in Analytic Number Theory, 2nd Edition by M. Ram Murty. (A phenomenal and digestible read!).
This would act as our guide in exploring topics, a place to practice problem solving and serve as a jumpstart to fostering questions we would like to answer in our own research.\[ \] \[ \] \[ \] \[ \] \[ \] \[ \] \[ \]
Tien, David and I then proceeded to meet once a week over the course of four months to discuss various things:
(Note: As this project had a lot of flexibility, Tien and I were also meeting on our own several times a week to discuss and work different parts of this project) \[ \] Getting to know each other and taking a look at David’s personal research. \[ \]\[ \]
Python code we used to reach conclusions seen in our presentation (graphs, square-free checks, etc.).
Utilizes NumPy and MatPlotLib, features unique functions:
Due to COVID 19, the 2021 DRP poster viewing/presentation session was hosted on Gather-Town.
From the 16 weeks, I personally developed these skills:
Thanks for coming on this journey with me!